Compared to bulk, guided-wave, and fiber-optic systems, photonic integrated circuits (PICs) can offer improved performance and stability in a smaller footprint, and at lower cost. Many applications such as communication network filters, multiplexers and de-multiplexers [1], optical-gyro-scope rotational-velocity sensors [2], optical buffers [3], bio-photonic sensing [4], low-noise microwave synthesizers, and quantum communication require resonators with large on-chip optical path length, ultralow propagation loss, and high quality factor [5].

The choice of waveguide materials determines the wavelength range, propagation loss, polarization sensitivity, and the degree of integration. Silicon-based materials are those most often used for biosensing applications. The main advantages of silicon-based photonic waveguides are low price and good optical quality of the silicon substrates. Moreover, they take advantage of the widely developed experience in microelectronic technology. Silicon wafers are provided with a silicon dioxide layer by deposition, or by oxidation of silicon at high temperature. The waveguide core is formed by further deposition of a high-index silicon nitride layer, usually via chemical vapor deposition. Additionally, silicon microelectronics allows high homo-geneity of the waveguide material, and the possibility of final integration in a lab-on-chip (LOC) device, enjoying the benefit of experience in microelectronic and semiconductor technology.

A major limitation of the silicon-on-insulator (SOI) material system is the fact that it cannot be used for applications operating at shorter wavelengths in the visible and sub-1.1-µm near-infrared regions [6]. However, this spectral region is the most relevant for life-science and health-related applications that offer strong potential for photonic integration. Examples include LOC systems for evanescent-field-based sensing detection [7] and fluorescence, and Raman spectroscopy [8]. For such applications, the visible and very-near-infrared (500~900 nm) wavelength window is of particular interest, due to its minimal photodamage to living cells, negligible water absorption, low fluorescence, and the availability of low-cost sources and sensitive silicon-based detectors.

Stoichiometric silicon nitride (Si₃N₄) offers higher refractive-index contrast with silicon dioxide (SiO₂) than other core materials, such as silicon oxynitride, phosphorusdoped SiO₂, or germanium-doped SiO₂, and offers the benefits of increased material stability and high refractive-index regularity. Therefore, Si₃N₄ for the core and SiO₂ for the cladding could be a suitable choice, because of the large refractive index difference, low scattering loss, wide transparency window, and compatibility with Si microelectronic technology. Moreover, silicon nitride films deposited with low-pressure chemical vapor deposition (LPCVD) have thickness that is controllable to the nanometer scale, and exhibit the low surface roughness (<0.4 nm) and quality necessary for maintaining low scattering-loss scales at the top and bottom core-cladding interfaces [9-12].

The bimodal evanescent-wave interferometric biosensor proposed in this paper simplifies the fabrication process of the Mach-Zehnder interferometric biosensor while maintaining the benefits inherent to integrated-optical (IO) biosensors based on interference, such as sensitivity, low-cost production through standard CMOS-compatible processes, and a high level of integration.

To compare different integrated-optical biosensors, the limit of detection (LOD) has become a standard indicator of performance. However, in terms of real-life applications, it is worthwhile to distinguish between bulk and surface sensitivity. The bulk sensitivity is the variation of the effective index of a guided mode induced by homogeneous variation of the index of the external cladding medium. Meanwhile, a thin-layer model can be adopted, since only a region smaller than the penetration depth of the guided mode is involved in the biological interaction process. In this case, the surface sensitivity is the variation of the effective refractive index of the guided mode as a function of the thickness of the biological layer. Table 1 shows the surface and bulk LODs for different biosensors, for an assumed refractive index n = 1.45 of a protein molecular layer.

As shown in Table 1, the bimodal waveguide biosensor is one of the most sensitive in terms of surface LOD, and at the same time offers a much simpler fabrication process and integration feasibility, compared to the other biosensors. This is the main reason why the bimodal biosensor is one of the most promising IO biosensors.

In this paper we derive the geometrical aspect ratio for the single-mode conditions for an Si₃N₄ rib optical waveguide, utilizing the effective-index method [13] and the Goos-Haenschen shift [14], and observe the effective refractive index as a function of rib-waveguide width, rib-core thickness, and rib-etching thickness, based on the numerical film-mode-matching method, for a wavelength of 0.63 µm. Finally, we propose a bimodal (two-mode) interferometer structure based on the rib-optical waveguides, for evanescent-wave biosensor applications [15, 16].

Silicon nitride rib optical waveguides are attractive candidates for photonic biosensors, because of the high intrinsic sensitivity of the photonic sensor itself, suitability for high-volume manufacturing, and integration into photonic-fluidic devices [17]. The interaction between light and the material to be measured occurs through refractive-index sensing. Therefore, the waveguide’s top cladding is locally removed, such that the optical field is in contact with the analyte. To achieve high sensitivity of the biosensor and coupling to an optical fiber, the rib optical waveguide should be designed and fabricated to provide the intrinsic characteristics for a photonic biosensor, as mentioned. On the other hand, the single-mode conditions for a rib-optical waveguide tend to be considered very similar to the single-mode conditions for a slab optical waveguide, but it will be seen that they are substantially different [18].

Figure 1 shows the cross section and dimensions of the rib optical waveguide analyzed here. The rib width and inner height are designated as W and H respectively, and the outer region of the rib has thickness h. The three dielectric materials (such as Si₃N₄, SiO₂, and Si substrate) have refractive indices of n₁, n₂, and n_s respectively. n₃ is the refractive index for the specific cover material (air, water, SiO₂, specific solution, etc.). The rib-guide modes are denoted as TEnm or TMnm (n, m = 0, 1, 2...), with TE being horizontally polarized and TM vertically polarized. We restrict our consideration to a rib waveguide with 0.5 ≤ h/H ≤ 1.

For the analysis of the rib optical waveguide, it is convenient to introduce an effective parameter as below:

The effective width and height of rib and planar waveguide in Fig. 1 are defined based on the Goos-Haenschen shift [14] as

The condition that the higher-order modes are blocked, including the first higher-order mode of the TE mode in Eq. (1), can be expressed as follows, using the reference document [18, 19]:

Therefore, the condition V < Vs must be satisfied to guarantee single-mode transmission in the rib optical waveguide. In this case, the geometrical ratio w_eff / H_eff is derived as below:

When Eqs. (2)~(4) are applied to Eq. (6), the conditions for the propagation of a single mode are as follows:

On the other hand, in the structure shown in Fig. 1, the middle-rib and two-sided-slab structures transmit at least one mode, and we derive the geometric ratio h_eff / H_eff, which guarantees single-mode transmission, utilizing the effective-refractive-index method [13], under the assumption that the slab optical waveguide is not limited to a single mode. It has been mentioned that the single-mode conditions of the rib optical waveguide are not identical to those for the slab optical waveguide, as described by Soref et al. [18]. That is, even in a single mode in the horizontal direction in the rib optical waveguide structure satisfying V < Vs, higher-order modes may exist in the vertical direction, and the intensity distribution of these higher-order modes show at least two vertical peaks. In this case, one of the peaks of the higher-order modes in the rib optical waveguide is coupled to the fundamental mode of the slab optical waveguide located around the rib optical waveguide, and eventually converted into a leaky mode. Therefore, when the ratio of the width w and height H of the rib structure is appropriately adjusted, the single-mode transmission characteristic can be obtained; this was verified in reference [19] by applying the beam-propagation method (BPM). The effective refractive index of the first higher-order mode in the rib region must be smaller than the effective refractive index of the basic mode in the slab region, and can be expressed by the following equation [20]:

Eventually, h_eff / H_eff is derived as follows:

Therefore, only when conditions (7) and (9) are satisfied simultaneously, the rib optical waveguide ultimately exhibits the single-mode characteristic.

We examine the influences of wavelength, etched rib thickness, rib width, and rib-core thickness on the effective refractive indices and mode patterns of the guided modes in the rib optical waveguide, with concrete refractive indices and dimensions as shown in Fig. 2. “Fimmwave Mode Solver” software from Photon Design was used for computer simulations [21].

The rib optical waveguide’s width W is varied from 1 to 10 µm, to examine its effect on the effective refractive indices of the fundamental and higher-order modes, for rib thickness of 10, 20, and 30 nm as a parameter. The simulation results in Fig. 3 show that the rib width should be less than about 1.5 µm to maintain a single mode, for 10-nm rib thickness. As the rib thickness increases, multi-mode characteristics are observed. The refractive-index change according to rib-thickness variation in the fundamental mode (TE00) is not so large, compared to that for the high-order modes TE01 and TE02, but changes gradually.

In Fig. 4, the rib thickness T (as shown in Fig. 2) is varied from 1 to 10 nm, to study its effect on the effective refractive indices of the guided modes for rib widths of 3, 5, and 10 µm respectively, as a parameter. We observe that the effective refractive indices of guided modes tend to decrease gradually as the rib thickness increases, because as the thickness rises a larger portion of the guided mode is in contact with the upper cladding material, which has a lower refractive index. Therefore, as the rib thickness and rib width increase, the portions contacting the cladding material become larger, and the refractive indices decrease steeply for the first and second higher-order modes (TE01 and TE02), as shown in Fig. 4.

The core thickness H (as shown in Fig. 1) is varied from 100 to 400 nm, to study its effect on the effective refractive indices of the guided modes for the combinations of rib width (µm) and thickness (nm) of (4, 2), (10, 10), and (10, 50) respectively, as parameters. As shown in Fig. 5, the effect of the core thickness on the effective refractive index is very small, regardless of the width and thickness of the rib optical waveguide. There is almost no difference in the effective refractive indices between the fundamental mode and the high-order modes, as shown in Fig. 5(a). As the core thickness increases, a minute change in effective refractive index between the modes is detected, as shown in Figs. 5(b) and 5(c). That is, since the guided modes in the rib structure are distributed just immediately under the rib, the core thickness does not significantly affect the effective refractive index.

An optical wave propagates through the waveguide’s rib core, producing an evanescent wave at the substrate and cladding boundaries. Most photonic label-free biosensors are based on the evanescent-field detection principle. If a sensing window is etched in the cladding, opening access to the core’s surface, the properties (effective refractive index, phase, and intensity) of the guided modes in the core are directly related to any perturbation taking place in the evanescent area over the surface, as depicted in Fig. 6, which shows the two-mode interferometric biosensor configuration based on an evanescent wave. Light is confined to an input rib waveguide designed to support a single transverse mode, as shown in Fig. 6. After traveling along the single-mode rib waveguide, this fundamental mode is coupled into another rib waveguide that supports two transverse modes. Due to the vertical rib-core asymmetry introduced in the junction between the single and two-mode waveguides, the first-order mode is excited, and eventually two modes (the fundamental and first-order mode) propagate up to the output port of the chip. Therefore, we suggest a photonic evanescent-field biosensor based on the two-mode interferometric principle, utilizing Si₃N₄ rib waveguides.

The sensing window is opened at the two-mode waveguide of the device, to allow the interaction of the evanescent field with external material. The variation of the external refractive index affects the effective refractive indices N_TE0 and N_TE1 of the two modes, respectively via the evanescent fields of each. Due to the different confinement of each mode in the core of the two-mode waveguide, they are affected differently by the change in the external refractive index, thus creating a phase difference (namely, an interference pattern) at the exit of the device, according to Eq. (10) below:

where L is the length of the sensing area, ΔN_eff is the effective-index difference between two modes, N_TE0 and N_TE1 are the effective refractive indices of the fundamental and first modes respectively, and λ is the wavelength.

The refractive index of a material is highly dependent on the temperature. Therefore, the device has an intrinsic sensitivity to temperature changes, because the effective refractive index of each mode is differently affected. This is a drawback compared to the MZI configuration, in which the reference and sensing arms are equally affected by a temperature change [22]. However, this problem can be easily solved by incorporating a thermoelectric cooler (TEC) into the sensor module.

The parameters for single-mode and two-mode rib structures, such as materials and thickness, are chosen to obtain a high contrast in the output signal by performing film-mode-matching analysis. For the input single-mode waveguide, rib thickness, rib width, and core thickness are set to 2 nm, 3 µm, and 150 nm respectively, and the cover cladding material is SiO₂ (n = 1.46). The effective refractive index is simulated by varying the rib width, and it is confirmed that the waveguide with 3 µm shows a single mode, as seen in Fig. 7. The effective refractive index N_eff and confinement coefficient Г of the fundamental mode are calculated to be 1.7339 and 0.904 respectively. Therefore, it is confirmed that the fundamental mode is tightly constrained to the input rib waveguide.

The rib thickness, core thickness, and rib width for the two-mode rib waveguide, including the sensing area, are set to 2 nm, 340 nm, and 3 µm respectively, and H₂O (n = 1.33) is applied as the cover cladding material. The effective refractive index of guided modes with respect to the rib-width variation is shown in Fig. 8, from film-mode-matching (FMM) analysis. It is confirmed that the two modes are guided for a rib width of 3 µm, and the effective refractive indices and confinement coefficients of the fundamental and first modes are calculated as 1.8906, 1.8871, 0.904, and 0.578 respectively. The confinement values indicate that the fundamental mode is less sensitive to the upper cladding layer’s parameters, as more energy is located inside the core of the waveguide than for the first-order mode. As a result, the interaction of the first mode with the external medium when traveling along the sensor area is stronger than for the fundamental, which is more confined in the core. The optical influences on the evanescent fields of the two modes are different, depending on the species and concentration of the biomaterial contained in the H₂O solution in the sensing area, ultimately leading to a phase difference between the two modes. Therefore, we can identify material and measure concentration through proper analysis of the phase difference.

Fimmwave and Fimmprop optical-mode solvers (Photon Design, UK [19]), which rely on the FMM and eigenmode-expansion (EME) methods respectively, are used to estimate beam propagation along the proposed photonic sensing device, consisting of the single- and double-mode rib waveguides with specific thicknesses and indices in each section, as shown in Fig. 9. We can confirm that a Si₃N₄ thickness of 150 (340) nm leads to single- (double-) mode behavior, for a rib width of 3 µm.

The interference between both guided modes can be collected by a commercial two-section photodetector at the end of the device. Upon a biomolecular binding event, the refractive index on the surface will change, inducing a change in the effective refractive index of each mode. Therefore, since both modes have different propagation constants, the phase shift experienced by each mode will be different, providing an intensity variation across the vertical axis. The phase shift produced by a variation in the refractive index of the sensing area is quantified by monitoring the output intensity distribution measured in the two-section photodetector. The interferometric signal S_R(t) can be given by

where V is the fringe amplitude and I_up and I_down are the currents measured by the upper and lower sections of a two-section photodiode. ΔФ(t) is defined in Eq. (10).

In this work we derive and characterize the single-mode geometrical condition h_eff / H_eff > 0.5 for a Si₃N₄ rib optical waveguide structure suitable for evanescent-wave photonic biosensors, utilizing the effective optical waveguide parameter V and the Goos-Haenchen shift. The influences of wavelength, rib thickness, and rib width on the effective refractive index, mode profile, and propagation of the fundamental and first modes in the rib optical waveguide are systematically investigated by applying the film-mode-matching method.

Simulation indicates that a rib-core thickness of 150 nm, a rib height of 2 nm, and a slab height of 148 nm would provide single-mode conditions for a 3 µm wide rib and SiO₂-clad waveguide at a wavelength of 0.63 µm. The effective refractive index and confinement coefficient of the fundamental mode are calculated to be 1.7339 and 0.904 respectively. A rib-core thickness of 340 nm, a rib height of 2 nm, and a slab height of 338 nm for the sensing region provide two-mode conditions for a 3 µm wide rib and H₂O-clad waveguide. The effective refractive indices and confinement coefficients of the fundamental and first modes are calculated as 1.8906, 1.8871, 0.904, and 0.578 respectively.

The confinement values indicate that the fundamental mode is less sensitive to the upper cladding layer’s parameters, as more energy is located inside the core of the waveguide than for the first-order mode. As a result, the interaction of the first mode with the external medium while traveling along the sensor area is more sensitive than for the fundamental, which is more confined to the core. Therefore, the optical influence on the evanescent fields of the two modes is different, depending on the species and concentration of the biomaterial contained in the H₂O cladding solution in the sensing area, ultimately leading to a phase difference between the two modes. Ultimately, by properly analyzing this phase difference, the type and concentration of the biomaterial can be determined.

This paper has focused on the modal analysis of silicon nitride rib waveguides, and the design of a rib-waveguide structure for a bimodal evanescent-wave interferometric biosensor. The proposed sensor can be fabricated utilizing silicon-photonics foundries (nanofabrication process) that are commercially available, based on multichip projects (MCPs).